Signed networks form a particular class of complex networks that has many applications in sociology, recommender and voting systems. The contribution of this paper is twofold. First, we propose an approach aimed at determining the characteristic subgraphs of the network. Second, we apply the developed approach to the analysis of the network describing the Wikipedia adminship elections. It is shown that this network agrees with the status theory if one does not consider strongly tied vertices, i.e., the vertices that are connected in both directions. At the same time, the strongly connected vertices mostly agree with the structural balance theory. This result indicates that there is a substantial difference between single and double connections, the fact that deserves a detailed analysis within a broader context of directed signed networks.